Migração FD 3D em profundidade usando aproximação de Padé complexa

Abstract

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performace and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardizes correct positioning of dipping reflectors in the directions not used for the splitted operators. We implement 3D downward continuation migration without splitting in the space coordinates using a complex Padé approximation and implicit finite differences. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large banded linear system. We compare the performance of the iterative stabilized biconjugate gradient (Bi-CGSTAB) and the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation provides an effective preconditioner for the Bi-CGSTAB, reducing the number of iterations relative to the real Padé expansion of the FD operator. As a consequence, the iterative Bi-CGSTABmethod ismore efficient than the directMUMPSmethodwhen solving for a single termin the Padé expansion. Forwide angle approximations direct methods are required. These algorithms are validated and the properties evaluated computing themigration impulse response in the SEG/EAGE salt model.